Find the boundary between a mixture and all liquid

An ideal vessel contains 0.100 kg ice at −10°C. Add 0.200 kg water at an adjustable initial temperature T. Use ci = 2100 J/(kg·K), cw = 4200 J/(kg·K), and Lf = 334000 J/kg.

What minimum initial water temperature just melts all the ice at equilibrium?

Organize the givens & assumptions

Ice = 0.100 kg at −10°C
Added water = 0.200 kg
Final state at threshold: all liquid at 0°C
ci = 2100; cw = 4200; Lf = 334000 in SI units

Ideal insulated calorimetry at ordinary atmospheric pressure, no evaporation or other work, equilibrium final state and stated constant model capacities unless a temperature dependence is specified. Vessel heat capacity is negligible except where it is an explicit unknown. Pure ice/water melts at 0°C; no supercooling.

A $2.50^\circ\mathrm C$
B $42.26^\circ\mathrm C$
C $39.76^\circ\mathrm C$
D $28.17^\circ\mathrm C$

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